An important thing to remember about any historical era, like the classical, renaissance, early modern, modern, medieval etc, is that there are often no hard or sharp distinctions between them. People did not wake up one day and check their calendars and see that the classical era was over and that they were medieval now. Rather, these are terms historians created after the fact to construct an overall framework to signal general large changes. As such, they are more useful for understanding how we think about these time periods as opposed to what actually happened or how people thought.

So why do we differentiate between the Middle Ages and the classical period? Part of the answer to this question is that for a long time there was a linear teleological concept of history. In simpler terms, historians believed that history and civilization was constantly moving towards “progress” and science away from barbarism and the “irrational”. The fall of Rome caused a big problem for this viewpoint, as Rome was seen as the next step in a line of “progress” from the Greeks. The fall of Rome and the onset of the Middle Ages interrupted “progress” and was seen as a step backward. Thus, a distinction was made between the “progress” of the Romans and the perceived lack of progress during the middle ages.

This view of the middle ages as its own distinct era was reinforced by enlightenment and renaissance thinking. The men of these periods saw themselves as reaching back and rediscovering the ideas and values of the ancients, and cast the time in between them and the Greeks and Romans as backwards and barbaric. They even went so far as to invent medieval practices to set themselves apart. For example, the idea of Prima Nocta, or the right of a lord to have intercourse with a woman before her wedding night, never actually happened during the middle ages. We have no records of this ever being an institutionalized practice. Instead, all the records and mentions of it we have all appear in enlightenment era writings. (This may not be true in its entirety and the debate is not settled from an academic standpoint. Thank you /u/TangosWithNapalm).

This is not to say that the distinction between the classical and the medieval are not still useful, and there were certainly many changes around the 4th and 5th centuries that would cause us to take note of particular changes during this time. However, these changes are not as “sharp” as you might expect. For example, Rome fell during the 4th and 5th centuries, although historians still debate the exact date of this event. Despite Rome’s collapse, many people in the early middle ages still used and considered themselves to be roman. For example, in Gregory of Tour’s History of the Franks he refers to many people in the 5th and 6th century as being of a senatorial class, even though medieval Gaul at this time was under the control of the Franks and no longer under Roman rule. In addition, many chronicles, such as John of Biclaro’s chronicle and the chronicle of 754, still refer to the Byzantine Emperor as the emperor of the romans. This indicates that for people of this time Rome, or at least something roman, was alive in the east.

TLDR: There certainly are distinctions and changes between the classical and medieval eras, but they are not as sharp as the change in era might make them first appear.

Follow up questions:

In Robin Pierson's "The History of Byzantium" podcast he mentions that the murder of Hypatia in Alexandria in 415 is used by some to mark the end of Classical Antiquity. Her wikipedia article also mentions this under the section about her death.

Was the death of Hypatia that significant a loss for the schools of classical antiquity as to mark the end of classical antiquity or is it more symbolic?

Justinian saw through reforms that strengthened state sponsored christianity and further eroded paganism (of all types including Hellenism) and classical philosophy including shutting down the school in Athens over a hundred years later in 529.

How long did classical philosophy survive after this as an active philosophy passed from teachers to students (and not simply through writings)?

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